User:Divenal/sandbox - Revision history

Divenal at 16:04, 5 August 2020

2020-08-05T16:04:31Z

← Older revision		Revision as of 16:04, 5 August 2020
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	# <math>1 \text{ radian} = \frac{180}{\pi} \text{ degrees} = \frac{60 \times 180}{\pi} \text{ arc-minutes} </math>		# <math>1 \text{ radian} = \frac{180}{\pi} \text{ degrees} = \frac{60 \times 180}{\pi} \text{ arc-minutes} </math>

	Acuity is a measure of the ability to resolve small details, defined by the "minimum angle of resolution". Normal vision ("20/20", or 1.0) is the ability to resolve features subtending 1 minute of arc.		Acuity is a measure of the ability to resolve small details, defined by the "minimum angle of resolution". Normal vision ("20/20", or 1.0) is the ability to resolve features subtending 1 minute of arc. In order to have a bigger-is-better score, the reciprocal of the angle is usually used:
	* On a [[Snellen chart]] the letters are defined on a 5x5 grid: the detail to be resolved to distinguish between characters is one pixel of that grid
	* On a Landolt C chart, the gaps in the circles, like the 'C's on the Snellen chart, are 1 minute of arc.

	In order to have a bigger-is-better score, the reciprocal of the angle is usually used:

	<math> \text{Acuity} = 1/A = \frac{pi}{60 \times 180} \times \frac{b}{a} = 0.00029 \times \frac{b}{a}</math>		<math> \text{Acuity} = 1/A = \frac{pi}{60 \times 180} \times \frac{b}{a} = 0.00029 \times \frac{b}{a}</math>
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	* -0.3 is "20/10" (2.0 or 0.5 arc-minutes)		* -0.3 is "20/10" (2.0 or 0.5 arc-minutes)

	On a Snellen chart, one ~~useful way~~ to ~~think~~ of the ~~labels on~~ the ~~letter rows~~ is as "~~the~~ distance ~~at which they subtend 5 arc~~-~~minutes~~".		On a [[Snellen chart]] the letters are defined on a 5x5 grid: the detail to be resolved to distinguish between characters is one pixel of that grid.
	~~On a~~ chart ~~designed~~ for ~~use at 20 feet, the letters on~~ the "20/50" line ~~are of such a height that they subtend 5 arc-minutes at a~~		Here 'b' is the distance to the chart (eg 6m) and 'a' is the height of the letters. It's not critical that the eye is at the bottom or top of a row of letters - as long as the angles remain small, the numerical error is insignificant.
	~~distance of 50 feet. By the various identities above~~, ~~they are 2.5~~ times ~~the~~ height of the "20/20" ~~letters~~, ~~and they subtend~~
	~~an angle of~~ 12.5 arc~~-minutes at 20 feet~~.		Acuity is reported in the form "distance/letter-row", such as "20/40", etc.

			<math> \text{Acuity} = 5 \times 0.00029 \times \frac{ \text{distance to chart}}{\text{letter height}}
			= \frac{ \text{distance to chart}}{690 \times \text{letter height}}</math>

			Then, for example
			* for the "6/12" line, we need <math>690 \times \text{height} = 12m \implies \text{height} = 12m / 690 = 1.73cm</math>
			* for the "20/15" line, we need <math>690 \times \text{height} = 15ft \implies \text{height} = 15 * 12 / 690 = 0.26 \text{inch}</math>

			The denominator can be interpreted as the distance at which the letters subtend 5 minutes of arc.

Divenal at 13:15, 5 August 2020

2020-08-05T13:15:42Z

Divenal at 15:03, 3 August 2020

2020-08-03T15:03:17Z

← Older revision		Revision as of 15:03, 3 August 2020
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	An alternative representation of acuity is "logMAR" ("log<sub>10</sub> Minimum Angle of Resolution"). This has a bigger-is-worse direction.		An alternative representation of acuity is "logMAR" ("log<sub>10</sub> Minimum Angle of Resolution"). This has a bigger-is-worse direction.
	* 0.0 corresponds to "20/20"		* 0.0 corresponds to "20/20" (1.0 or 1 arc-minute)
	* 1.0 is "20/200"		* 1.0 is "20/200" (0.1 or 10 arc-minutes)
	* -0.3 is "20/10"		* -0.3 is "20/10" (2.0 or 0.5 arc-minutes)

	On a Snellen chart, one useful way to think of the labels on the letter rows is as "the distance at which they subtend 5 arc-minutes".		On a Snellen chart, one useful way to think of the labels on the letter rows is as "the distance at which they subtend 5 arc-minutes".

Divenal at 15:01, 3 August 2020

2020-08-03T15:01:10Z

← Older revision		Revision as of 15:01, 3 August 2020
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	#* so for fixed angle, 'a' is proportional to 'b'		#* so for fixed angle, 'a' is proportional to 'b'
	# for very small angles (expressed in radians), <math>tan(A) \approx A</math>		# for very small angles (expressed in radians), <math>tan(A) \approx A</math>
	#* so at small angles, 'b' is proportional to 'A'		#* so at small angles, 'a' is proportional to 'A'
	# 1 radian = <math>\frac{180}{\pi}</math> degrees = <math>\frac{60 \times 180}{\pi}</math> arc-minutes		# 1 radian = <math>\frac{180}{\pi}</math> degrees = <math>\frac{60 \times 180}{\pi}</math> arc-minutes

Divenal at 14:55, 3 August 2020

2020-08-03T14:55:07Z

← Older revision		Revision as of 14:55, 3 August 2020
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	A reminder about some trigonometry / geometry		A reminder about some trigonometry / geometry
	# <math>tan(A) = \frac{a}{b}</math>		# <math>tan(A) = \frac{a}{b}</math>
			#* so for fixed angle, 'a' is proportional to 'b'
	# for very small angles (expressed in radians), <math>tan(A) \approx A</math>		# for very small angles (expressed in radians), <math>tan(A) \approx A</math>
			#* so at small angles, 'b' is proportional to 'A'
	# 1 radian = <math>\frac{180}{\pi}</math> degrees = <math>\frac{60 \times 180}{\pi}</math> arc-minutes		# 1 radian = <math>\frac{180}{\pi}</math> degrees = <math>\frac{60 \times 180}{\pi}</math> arc-minutes

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	In order to have a bigger-is-better score, the reciprocal of the angle is usually used.		In order to have a bigger-is-better score, the reciprocal of the angle is usually used.
	Acuity <math> = 1/A = \frac{pi}{60 \times 180} \times \frac{b}{a} = 0.00029 \times \frac{b}{a}</math>		Acuity <math> = 1/A = \frac{pi}{60 \times 180} \times \frac{b}{a} = 0.00029 \times \frac{b}{a}</math>



	An alternative representation of acuity is "logMAR" ("log<sub>10</sub> Minimum Angle of Resolution"). This has a bigger-is-worse direction.		An alternative representation of acuity is "logMAR" ("log<sub>10</sub> Minimum Angle of Resolution"). This has a bigger-is-worse direction.
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	* 1.0 is "20/200"		* 1.0 is "20/200"
	* -0.3 is "20/10"		* -0.3 is "20/10"

			On a Snellen chart, one useful way to think of the labels on the letter rows is as "the distance at which they subtend 5 arc-minutes".
			On a chart designed for use at 20 feet, the letters on the "20/50" line are of such a height that they subtend 5 arc-minutes at a
			distance of 50 feet. By the various identities above, they are 2.5 times the height of the "20/20" letters, and they subtend
			an angle of 12.5 arc-minutes at 20 feet.

Divenal at 09:53, 2 August 2020

2020-08-02T09:53:31Z

← Older revision		Revision as of 09:53, 2 August 2020
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	# 1 radian = <math>\frac{180}{\pi}</math> degrees = <math>\frac{60 \times 180}{\pi}</math> arc-minutes		# 1 radian = <math>\frac{180}{\pi}</math> degrees = <math>\frac{60 \times 180}{\pi}</math> arc-minutes

	"20/20" ~~acuity~~ is ~~defined as~~ the ability to resolve ~~details which subtend~~ 1 arc~~-minute at~~ the ~~eye.~~		Acuity is a measure of the ability to resolve small details, defined by the "minimum angle of resolution". "20/20", or 1.0, is the ability to resolve features subtending 1 minute of arc.
	~~So if~~ 'A' is 1 arc-~~minute and 'b'~~ is ~~the distance to the object~~, ~~then~~ the ~~height 'a'~~ of the ~~object is~~		* On a [[Snellen chart]] the letters are defined on a 5x5 grid: the detail to be resolved to distinguish between characters is one pixel of that grid
	is		* On a Landolt C chart, the gaps in the circles, like the 'C's on the Snellen chart, are 1 minute of arc.
	<math>a = \frac{60 \times 180~~}{pi~~} \times b = 0.00029 \times b</math>
			In order to have a bigger-is-better score, the reciprocal of the angle is usually used.
			Acuity <math> = 1/A = \frac{pi}{60 \times 180} \times \frac{b}{a} = 0.00029 \times \frac{b}{a}</math>



			An alternative representation of acuity is "logMAR" ("log<sub>10</sub> Minimum Angle of Resolution"). This has a bigger-is-worse direction.
			* 0.0 corresponds to "20/20"
			* 1.0 is "20/200"
			* -0.3 is "20/10"

Divenal at 21:44, 1 August 2020

2020-08-01T21:44:49Z

← Older revision		Revision as of 21:44, 1 August 2020
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	This combines the two ideas... It's sized to suit my smartphone, but feel free to make your custom version as above.		This combines the two ideas... It's sized to suit my smartphone, but feel free to make your custom version as above.

			<br clear="both" />

			----

			[[File:TrigonometryTriangle.svg\|right\|TrigonometryTriangle]]

			A reminder about some trigonometry / geometry
			# <math>tan(A) = \frac{a}{b}</math>
			# for very small angles (expressed in radians), <math>tan(A) \approx A</math>
			# 1 radian = <math>\frac{180}{\pi}</math> degrees = <math>\frac{60 \times 180}{\pi}</math> arc-minutes

			"20/20" acuity is defined as the ability to resolve details which subtend 1 arc-minute at the eye.
			So if 'A' is 1 arc-minute and 'b' is the distance to the object, then the height 'a' of the object is
			is
			<math>a = \frac{60 \times 180}{pi} \times b = 0.00029 \times b</math>

Divenal at 09:38, 22 July 2020

2020-07-22T09:38:50Z

← Older revision		Revision as of 09:38, 22 July 2020
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	[[Wikipedia:Scalable_Vector_Graphics\|SVG]] is a simple xml markup system for describing images. (Well, simple for the trivial stuff I'm using it for...) You just tell it "I want a blue circle here, a red square there, ...". Unlike a bitmap, this will render perfectly at any scale. But obviously you need software to turn it into bitmap of the size you need. The wiki will do so itself, ~~but~~ I'm not quite sure if it renders it for each size, or if it renders it once on upload and just rescales the bitmap.		[[Wikipedia:Scalable_Vector_Graphics\|SVG]] is a simple xml markup system for describing images. (Well, simple for the trivial stuff I'm using it for...) You just tell it "I want a blue circle here, a red square there, ...". Unlike a bitmap, this will render perfectly at any scale. But obviously you need software to turn it into bitmap of the size you need.

			The wiki will do so itself. You can add a reference to the image from your own wiki page and tell it what size to display. Just add a reference of the form <nowiki>[[File:filename.svg\|512px]]</nowiki>. The 512px is the image size you want, and you can set that to whatever you want. (I'm not quite sure if it renders it for each size, or if it renders it once on upload and just rescales the bitmap. Not sure if the wiki has an option to just pass the svg directly to the browser for rendering..?) see https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Images

			Modern browsers can generate svg directly. If you click on one of the images, it will take you to the wiki page about the file. Clicking again should present the svg directly to the browser for local rendering. Resizing there should be accurate since it should re-render from the vector description. You can use the browser's view-source option to see the (trivial) svg that creates the image. It should be fairly obvious how it works. The only slightly non-trivial thing is the <nowiki><g ...></nowiki> stuff. I tend to use that to move the origin to the centre of the canvas, and various other convenient defaults, to save having to repeat stuff on every line.

	There are some online convertors you can use. Just google.		There are some online convertors you can use. Just google.
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	Also the distance at which ghosting first appears, if you're also measuring that. For me, the ghosting appears in particular directions, so you can concentrate on the gaps on the lines where the ghost image is most-separated from the original. (ie if ghosting happens in a north-east direction, look at the gaps on the lines going north-west.)		Also the distance at which ghosting first appears, if you're also measuring that. For me, the ghosting appears in particular directions, so you can concentrate on the gaps on the lines where the ghost image is most-separated from the original. (ie if ghosting happens in a north-east direction, look at the gaps on the lines going north-west.)

			<br clear="both" />
	----		----

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	This is a quick svg hack-up of the test page on [[Varakari's_Vision_Log_Tool]]. My intention was to be able to display it on my smartphone for measurement, but should work on any browser.		This is a quick svg hack-up of the test page on [[Varakari's_Vision_Log_Tool]]. My intention was to be able to display it on my smartphone for measurement, but should work on any browser.

	The image itself is svg, and so infinitely scalable. But the wiki tends to generate it as a png. So if you need to resize it, it's better to do it as svg rather than zooming in or out of the png. One simple way to do that is to add a reference to the image from your own wiki page, and adjust the size. Then the wiki will generate a png at that size, and you can download it locally.

	To do so, just add a reference of the form <nowiki>[[File:rgfocus.svg\|512px]]</nowiki>. The 512px is the image size you want, and you can set that to whatever you want. The wiki should render the svg to a bitmap of that size. (The original is 256px.) There are various other options that can go in - see https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Images

	If you click on the image, it will take to the page about the file. Clicking again should present the raw svg to the browser. You can use the browser's view-source option to see the (trivial) svg that creates the image. It should be fairly obvious how it works. The only slightly non-trivial thing is the <nowiki><g ...></nowiki> stuff. That just moves the origin to the centre of the canvas and sets the default text anchor, so that all the entities have an x-co-ord of 0. Just saves having to repeat stuff on every line.

	Do feel free to improve it.		Do feel free to improve it.

			<br clear="both" />
	----		----

Divenal at 13:54, 20 July 2020

2020-07-20T13:54:35Z

← Older revision		Revision as of 13:54, 20 July 2020
Line 1:		Line 1:
	Welcome, {{#ifanon:anonymous\|registered}} user.		Welcome, {{#ifanon:anonymous\|registered}} user.


			[[Wikipedia:Scalable_Vector_Graphics\|SVG]] is a simple xml markup system for describing images. (Well, simple for the trivial stuff I'm using it for...) You just tell it "I want a blue circle here, a red square there, ...". Unlike a bitmap, this will render perfectly at any scale. But obviously you need software to turn it into bitmap of the size you need. The wiki will do so itself, but I'm not quite sure if it renders it for each size, or if it renders it once on upload and just rescales the bitmap.

			There are some online convertors you can use. Just google.

			If you want to do it locally, one free application (both windows and linux) is [[wikipedia:Inkscape\|Inkscape]]. You can either load the svg file interactively and then export via the menus, or use a command line:
			inkscape -w 1024 -h 1024 input.svg --export-filename output.png

			Another free command-line tool is [[wikipedia::ImageMagick\|ImageMagick]]
			convert -size 1024x1024 input.svg output.png

			----

	[[File:Dd_blur_tool.svg\|480px\|thumb\|right\|click to enlarge]]		[[File:Dd_blur_tool.svg\|480px\|thumb\|right\|click to enlarge]]

Divenal at 17:19, 15 July 2020

2020-07-15T17:19:11Z

← Older revision		Revision as of 17:19, 15 July 2020
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	[[File:Dd_blur_tool.svg\|~~200px~~\|thumb\|right\|click to enlarge]]		[[File:Dd_blur_tool.svg\|480px\|thumb\|right\|click to enlarge]]

	This is a tool that might be useful for distingushing https://endmyopia.org/astigmatic-cylinder-blur-vs-myopic-spherical-blur/		This is a tool that might be useful for distingushing https://endmyopia.org/astigmatic-cylinder-blur-vs-myopic-spherical-blur/
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	----		----

	[[File:rgfocus.svg\|thumb\|right]]		[[File:rgfocus.svg\|256px\|thumb\|right]]

	This is a quick svg hack-up of the test page on [[Varakari's_Vision_Log_Tool]]. My intention was to be able to display it on my smartphone for measurement, but should work on any browser.		This is a quick svg hack-up of the test page on [[Varakari's_Vision_Log_Tool]]. My intention was to be able to display it on my smartphone for measurement, but should work on any browser.
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	----		----

	[[File:rgsunrise.svg\|thumb\|right]]		[[File:rgsunrise.svg\|384px\|thumb\|right]]

	This combines the two ideas...		This combines the two ideas... It's sized to suit my smartphone, but feel free to make your custom version as above.

← Older revision		Revision as of 13:15, 5 August 2020
Line 50:		Line 50:

	A reminder about some trigonometry / geometry		A reminder about some trigonometry / geometry
	# <math>tan(A) = \frac{a}{b}</math>		# <math>\tan(A) = \frac{a}{b}</math>
	#* so for fixed angle, 'a' is proportional to 'b'		#* so for fixed angle, 'a' is proportional to 'b'
	# for very small angles (expressed in radians), <math>tan(A) \approx A</math>		# for very small angles (expressed in radians), <math>\tan(A) \approx A</math>
	#* so at small angles, 'a' is proportional to 'A'		#* so at small angles, 'a' is proportional to 'A'
	# 1 radian = ~~<math>~~\frac{180}{\pi}~~</math>~~ degrees = ~~<math>~~\frac{60 \times 180}{\pi}</math> ~~arc-minutes~~		# <math>1 \text{ radian} = \frac{180}{\pi} \text{ degrees} = \frac{60 \times 180}{\pi} \text{ arc-minutes} </math>

	Acuity is a measure of the ability to resolve small details, defined by the "minimum angle of resolution". "20/20", or 1.0, is the ability to resolve features subtending 1 minute of arc.		Acuity is a measure of the ability to resolve small details, defined by the "minimum angle of resolution". Normal vision ("20/20", or 1.0) is the ability to resolve features subtending 1 minute of arc.
	* On a [[Snellen chart]] the letters are defined on a 5x5 grid: the detail to be resolved to distinguish between characters is one pixel of that grid		* On a [[Snellen chart]] the letters are defined on a 5x5 grid: the detail to be resolved to distinguish between characters is one pixel of that grid
	* On a Landolt C chart, the gaps in the circles, like the 'C's on the Snellen chart, are 1 minute of arc.		* On a Landolt C chart, the gaps in the circles, like the 'C's on the Snellen chart, are 1 minute of arc.

	In order to have a bigger-is-better score, the reciprocal of the angle is usually used.		In order to have a bigger-is-better score, the reciprocal of the angle is usually used:
	~~Acuity~~ <math> = 1/A = \frac{pi}{60 \times 180} \times \frac{b}{a} = 0.00029 \times \frac{b}{a}</math>
			<math> \text{Acuity} = 1/A = \frac{pi}{60 \times 180} \times \frac{b}{a} = 0.00029 \times \frac{b}{a}</math>

	An alternative representation of acuity is "logMAR" ("log<sub>10</sub> Minimum Angle of Resolution"). This has a bigger-is-worse direction.		An alternative representation of acuity is "logMAR" ("log<sub>10</sub> Minimum Angle of Resolution"). This has a bigger-is-worse direction.